A386926 a(n) = denominator(Sum_{k=1..n} d(k+1)/d(k)), where d is the number of divisors function.
1, 1, 2, 6, 6, 3, 3, 12, 4, 4, 4, 12, 12, 12, 6, 30, 30, 30, 30, 30, 30, 15, 15, 120, 120, 120, 120, 40, 40, 40, 40, 120, 120, 120, 120, 360, 360, 360, 360, 360, 360, 360, 360, 360, 360, 360, 360, 360, 360, 360, 360, 360, 360, 360, 360, 360, 360, 360, 360, 360, 360
Offset: 1
Examples
Fractions begin with 2, 3, 9/2, 31/6, 43/6, 23/3, 29/3, 125/12, 47/4, 49/4, 61/4, ...
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
- Florian Luca and Igor E. Shparlinski, On the values of the divisor function, Monatshefte für Mathematik, Vol. 154, No. 1 (2008), pp. 59-69.
Programs
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Mathematica
With[{s = DivisorSigma[0, Range[100]]}, Denominator[Accumulate[Rest[s]/Most[s]]]] -
PARI
list(nmax) = {my(s = 0, d1 = 1, d2); for(n = 2, nmax, d2 = numdiv(n); s += (d2/d1); print1(denominator(s), ", "); d1 = d2);}